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Q. If x i s real,then `(x^2+2x+c)/(x^2+4x+3c)` can take all real values if A)...
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High School Teacher
Given `(x^2+2x+c)/(x^2+4x+3c)` , determine the value(s) of c so that the expression can take all real values:
(A) Assuming the question means that you can put in any real value for x:
Suppose c=0: `(x^2+2x)/(x^2+4x)=(x(x+2))/(x(x+4))` . x cannot be zero so B and C are incorrect.
Suppose c=1: `(x^2+2x+1)/(x^2+4x+3)=((x+1)^2)/((x+1)(x+3))` . x cannot be -1 so A is incorrect.
The answer is D -- none of the above.
(B) Assuming the question meant that the expression could take on all real values (the output could be any real number) the answer is also D.
Posted by embizze on August 10, 2013 at 6:59 PM (Answer #2)
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